$$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right]$$$

この計算機は、$$$1$$$x$$$2$$$ 行列 $$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]$$$ に $$$2$$$x$$$1$$$ 行列 $$$\left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right]$$$ を掛け、手順を示しながら計算します。

入力内容

$$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right]$$$を計算せよ。

解答

$$$\left[\begin{array}{cc}{\color{Brown}\frac{\sqrt{2}}{2}} & {\color{DarkBlue}\frac{\sqrt{2}}{2}}\end{array}\right]\cdot \left[\begin{array}{c}{\color{Crimson}\frac{\sqrt{2}}{2}}\\{\color{BlueViolet}\frac{\sqrt{2}}{2}}\end{array}\right] = \left[\begin{array}{c}{\color{Brown}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{Crimson}\left(\frac{\sqrt{2}}{2}\right)} + {\color{DarkBlue}\left(\frac{\sqrt{2}}{2}\right)}\cdot {\color{BlueViolet}\left(\frac{\sqrt{2}}{2}\right)}\end{array}\right] = \left[\begin{array}{c}1\end{array}\right]$$$

解答

$$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2} & \frac{\sqrt{2}}{2}\end{array}\right]\cdot \left[\begin{array}{c}\frac{\sqrt{2}}{2}\\\frac{\sqrt{2}}{2}\end{array}\right] = \left[\begin{array}{c}1\end{array}\right]$$$A